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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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Computing the kernel of some Artin-Map
let $K = \mathbb{Q}(\sqrt{-5})$ and $L = K(i)$. $\mathcal{O}_K$ is the ring of integers of K.
I would like to show that the kernel of the Artin-Map $\phi_{L/K}: I_K \rightarrow Gal(L/K)$ is $P_K$, wh …